When a fight breaks out in a nightclub, one of the band members can be seen wearing a Black Flag shirt. This scene occurs in either 1976 or 1977, but Black Flag did not actually take the name Black Flag until 27 January 1979 (from 1976-1978 the band's name was Panic). Additionally, the song that is playing is a cover of the song Nervous Breakdown by Black Flag, which was not released until 1978.
The wide 7-ply laminate concave skateboard that Tyson the bulldog rides at the championship was not available in 1977. Laminate decks existed but they were flat and narrow. Skateboards in 1977 rarely exceeded 7-8 inches wide. Tysons board is obviously a 10 inch wide mid to late '80s pool/ramp model with wider trucks and "new school" wheels.
Early in the film, there's a scene where Jay, his mom and Sid are eating at the restaurant where Stacy works. Sid offers his American Express card to cover the meal. When the card is handed over, you can clearly see a magnetic stripe on the back. Magnetic stripes didn't exist on credit cards in the 70s.
Stacy makes an appearance in 'Charlie's Angels', a show which aired between 1976 and 1981. The episode she appears in is slated as "Episode # 93" which would make it 1979 (the year in which the real Stacy Peralta appeared in the show). Later, a TV newscast mentions the fire that finally devastated the partially-ruined (and out-of-operation) theme park, Pacific Ocean Park, that was built on and around the Ocean Park Pier. That catastrophic blaze (and there had been minor ones before it), actually happened in 1974, and had led to the demolition/removal of the theme park's remains in 1975.
When Stacey and Kathy leave after the first competition, they get in his car, and Stacey exclaims the Skip called him bro, and said, "You look hungry, bro." When really, Skip had said, "Hey, bro, you're lookin' hungry."
When Jay and Tony are in the bedroom with the two girls a stuffed animal is thrown and lands on the nightstand in front of the lamp. Tony's father comes in moments later asking about the smell in the air and the stuffed animal is gone.
At the end of the movie before tony Alva performs the front side air, Stacy is seen in the background standing, then when the camera angle changes and the scene pauses, he is on his knees petting one of the dogs.